Arithmetic and Geometric Sequences

Arithmetic or Geometric? Identify Common Difference/Ratio?

100

-4, 2, -1, 1/2

This is a Geometric sequence 

Common ratio: -1/2

200

2 1/2 , 3, 3 1/2, 4, 4 1/2...

What is Arithmetic?

Common Difference: 1/2

300

2, 4, 6, 8...

What is Arithmetic?

Common Difference: 2

400

-2, -4, -8, -16...

What is Geometric?

Common Ratio: 2

500

The sequence -5, -10, -15, -20

What is what is arithmetic?

Common Difference: -5

Common Difference

100

The Common Difference of -20, -23, -26, -29...

-3

200

The Common Difference of -1.7, -2.0, -2.3, -2.6...

-0.3 

300

The Common Difference of 18, 22, 26, 30...

4

400

The Common Difference of 100, 131, 162, 193...

31

500

^{The Common Difference of 2.53, 2.56, 2.59, 2.62...}

0.03

Common Ratio

100

The Common Ratio of the Sequence 2, 4, 8, 16, 32...

2

200

The Common Ratio of -1/2, 1, -2, 4...

-2

300

The Common Ratio of the Sequence 3, 9, 27, 81...

3

400

The Common Ratio of the Sequence -3, -1, -1/3...

1/3

500

The Common Ratio of the Sequence -1000, 200, -40, 8...

- 1/5 

Writing Equations (Geometric)

100

Write an equation for the nth term of the geometric sequences.

3, 15, 75, 375, 1875, ... 

a_n = 3(5)^n-1

200

Write an equation for the nth term of the geometric sequences. 

324, 108, 36, 12, 4, ...

a_n = 324(1/3)^n-1

300

Write an equation for the nth term of the geometric sequences. 

1, -2, 4, -8, 16, ....

a_n = 1(-2)^n-1

400

Write an equation for the nth term of the geometric sequences. Then find a₈

3, 6, 12, 24, ...

a₈ = 3(2)^8-1

a₈ = 3(2)

a₈ = 3(128) 

a₈ = 384

500

Write an equation for the nth term of the geometric sequences. Then find a₁₀

128, 64, 32, 16, 8, ...

a = 128(1/2)^10-1

a = 128(1/2)⁹

a = 128(1/512)

a = 128/512 or 0.25

Writing Equations (Arithmetic)

100

Write an equation for the nth term of the arithmetic sequences. 

1, 4, 7, 10, 13, ...

a_n = 1 + 3(n-1)

a_n= 1 + 3n - 3

a_n = 3n -2

200

Write an equation for the nth term of the arithmetic sequences. 

3, 8, 13, 18, 23, ...

a_n = 3 + 5(n-1)

a_n = 3 + 5n - 5

a_n = 5n -2

300

Write an equation for the nth term of the arithmetic sequences. 

-8, -2, 4, 10, 16, ...

a_n = -8 + 6(n-1)

a_n = -8 + 6n - 6

a_n = 6n - 14

400

Write an equation for the nth term of the arithmetic sequences. Then find a₇.

-6, 1, 8, 15, 22, ...

a₇ = -6 + 7(7 - 1) 

a₇ = -6 + 7(6)

a₇ = -6 + 42

a₇ = 36

500

Write an equation for the nth term of the arithmetic sequences. Find a₁₀

11, 4, -3, -10, -17, -24, ...

a₁₀ = 11 + -7(10-1)

a₁₀ = 11 + -7(9)

a₁₀ = 11 - 63

a₁₀ = -52